Experimental validation of mean-field bistability in the two-photon-pumped nuclear clock

Determine whether the bistability predicted by the mean-field equations for the two-photon-pumped collective cavity-QED nuclear clock represents genuine nonlinear dynamics, such as refractive optical bistability or few-atom cavity-QED bistability, rather than an artifact of the mean-field approximation.

Background

The paper analyzes a two-photon-pumped 229^{229}Th ensemble coupled collectively to a whispering-gallery-mode resonator. At sufficiently high pump powers, the mean-field steady-state equations predict a bistability region in which the nuclear excitation has two stable solutions separated by an unstable solution. The predicted clock instability can be discontinuous near this region because the optimal operating point may switch between the stable branches.

The authors note that experimentally accessing the more strongly excited stable branch may require deliberate state preparation, such as a strong pump pulse. It remains unresolved whether the predicted bistability is a physical nonlinear effect of the collective cavity-QED system or instead arises from the mean-field approximation used in the analysis.

References

Whether the predicted bistability represents genuine nonlinear dynamics---as in refractive optical bistability or few-atom cavity-QED systems---or instead arises from the mean-field approximation remains an open question for future experiments.

— Collective cavity quantum electrodynamics in solid-state optical clocks  (2609.24800 - Mamian et al., 21 Sep 2026) in Section “Two-photon-pumped clock,” paragraph discussing the bistability region and Fig. 3(c)